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Journal of Function Spaces and Applications
Volume 2012, Article ID 542607, 9 pages
http://dx.doi.org/10.1155/2012/542607
Research Article

On Divergence of Fourier Series by Some Methods of Summability

1Department of Mathematical Analysis, A. Razmadze Mathematical Institute, 1, Aleksidze Street, 0193 Tbilisi, Georgia
2Department of Mathematics, Georgian Technical University, 77, M. Kostava Street, 0175 Tbilisi, Georgia

Received 20 September 2010; Accepted 20 October 2010

Academic Editor: V. M. Kokilashvili

Copyright © 2012 Shakro Tetunashvili. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new summability method of series is introduced and studied. The particular cases of this method are, for example, variable-order Cesaro and Riesz methods. Applications to divergence problem of Fourier series are given. An extension of Kolmogorov, Schipp, and Bočkarev’s well-known theorems on divergence of Fourier trigonometric, Walsh, and orthonormal series is established.